Graph Theory Day is a semiannual one day event. Its purpose is to stimulate activity and interest among graph theorists by presenting timely and interesting talks by leading researchers. GTD42 was an opportunity to explore various software packages that in one way or another make or prove conjectures involving graph theory. There were demonstrations of conjecture-generating software and opportunities to try out the software.
The program also included time for the informal exchange of graph theory information, as well as a few short contributions to a Graph Theory Notes session.
This event kicked off the activities of the DIMACS Working Group on
Computer Generated Conjectures from Graph Theoretic and Chemical
The process of scientific discovery is a very complex one. Computers can aid human beings in the process and, as has been a goal of researchers in artificial intelligence, in an automatic way. In the mathematical sciences, discovery can be thought to have three components: development of conjectures, formation of new concepts, and proving of theorems or disproving of conjectures. There has been a large amount of research done on automatic theorem proving. Here, we concentrated on the use of the computer as a tool in generating conjectures, whether in an automated way or as a tool used interactively by a person.
Over the years, a variety of programs have been written to produce mathematical conjectures, either automatically or interactively. Some of these programs have led to very interesting new conjectures and new theorems. An area of particularly widespread activity and interest recently has been graph theory and related areas of chemistry. Researchers from a variety of groups around the world have been working in this area and are engaged in the tasks of using computational power to develop new conjectures, eliminate uninteresting ones, publicize the remaining conjectures, and aid in their solution by working scientists, with or without the aid of the computer. Many of these efforts start with large databases, for example of graph invariants and of relations among them, or of chemical structures. We brought together a group of researchers working on computer generated conjectures from graph-theoretic and chemical databases, including developers of some of the most important programs being used, to share their ideas and systems and initiate joint research efforts.
The primary goals of the working group was to foster an interchange of ideas among those working on different approaches to the use of computers to generate scientific conjectures, mainly in graph theory and in chemistry, and to initiate new collaborative research in this area. We encouraged exchange of views both about methods and about specific conjectures. Among the questions addressed were the following: